Short answer: there are no restrictions in principle on which amino acids can follow which. That means that in principle you can have polypeptide in any configuration: AAAA, WQWQWQ etc.
Problem is that polypeptides must be functional and, because they are in aqueous solution, it puts restrictions on how polypeptide form secondary and tertiary structure. It means that having very rigid hydrophobic surface is energetically unfavorable. If cell where to produce such polypeptide, it might be either degraded or cause problems for cell, such as aggregates or other form of toxicity.
That means that polypeptides has more restrictions than just linkage (C-N bonding) order. And of course it has been studied: Probabilistic analysis of the frequencies of amino acid pairs within characterized protein sequences.
Authors analyzed protein databases to find out which doublets of amino acids are more and less common. First of all, not all amino acids (of which there are 20 considered) have same occurrence, e.g. P(L, leucine)=0.096, P(W, tryptophan)=0.0118.
And, of course, not doublets are equally distributed (16 pairs out of 400 were picked as statistically significant):